Minimum-Cost Forest for Uncertain Multicast with Delay Constraints

The use of multicast transmission can efficiently reduce the consumption of network resources by jointly serving multiple destinations with a single source node. Currently, many multicast applications impose the constraint wherein multicast flows must be processed by a series of Virtual Network Functions (VNFs) before reaching their destinations. Given a multicast transmission, there are usually multiple server nodes, each of which is able to host all the required VNFs. Thus, the multicast flow should be initially steered to one or a few selected server nodes that act as pseudo sources, and the destinations will then retrieve new flow from any of these pseudo sources. In this paper, we model this kind of multicast as an uncertain multicast with multiple pseudo sources, whose routing structure is usually a forest consisting of multiple isolated trees. We then characterize and construct the Delay-guaranteed Minimum Cost Forest (D-MCF) such that each path from the source to the destination satisfies the end-to-end delay constraint. To tackle this NP-hard problem, we design two efficient methods, the Partition Algorithm (PA) and the Combination Algorithm (CA), to approximate the optimal solution. Theoretical analyses and evaluations indicate that these two methods can generate the desired routing forest for any multicast transfer. Moreover, the PA method achieves a better balance between performance and time consumption than the CA method. The evaluation results show that PA- $\mathrm{(}\mathrm{\Omega }\mathrm{+}\mathrm{20}\mathrm{)}$ can reduce total cost by $\mathrm{49.02}\mathrm{\%}$ while consuming $\mathrm{12.59}\mathrm{\%}$ more time, thus significantly outperforming the CA- $\mathrm{(}\mathrm{\Omega }\mathrm{+}\mathrm{20}\mathrm{)}$ method.